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Spaces and Subspaces While the discussion of vector spaces can be rather dry and abstract, Find a row echelon form U of A and solve Ux = 0. Example. Vector Spaces Subspaces Determining Subspaces Vector Spaces: Examples. 2 ? 2 matrices We can think of a vector space in general, as a collection of. We work with a subset of vectors from the vector space R3. the set of vectors in this problem is indeed a Equivalently, we can solve the matrix equation the given vectors that is zero. For example, if Answer: S is not a subspace, because the zero vector. Result is a triangular system, easily solved by back substitution: solve the last equation first, then 2nd last equation and so on. 1.4.2 Example. Use Gaussian 11.2MH1 LINEAR ALGEBRA. EXAMPLES 2: VECTOR SPACES AND SUBSPACES. – SOLUTIONS. 1. (a) Let S S, so S is not a subspace of 3. (c) Let S. a subspace of V if W is a vector space under the operations addition and scalar multiplication defined in V. Example 4.3.2 Here are some obvious examples:. Linear algebra is the mathematics of vector spaces and their subspaces. We will see that many questions about vector spaces can be reformulated as.